Question: Simplify the following expression: $\sqrt{150}+\sqrt{24}+\sqrt{96}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{150}+\sqrt{24}+\sqrt{96}$ $= \sqrt{25 \cdot 6}+\sqrt{4 \cdot 6}+\sqrt{16 \cdot 6}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{6}+\sqrt{4} \cdot \sqrt{6}+\sqrt{16} \cdot \sqrt{6}$ $= 5\sqrt{6}+2\sqrt{6}+4\sqrt{6}$ Finally, simplify by combining the terms. $= ( 5 + 2 + 4 )\sqrt{6} = 11\sqrt{6}$